Bernard Cohen was born to an Orthodox Jewish family in 1933 in London, where he still lives and works. He studied at South West Essex Technical College in 1949 before training at St Martin’s School of Art (1950–51) and the Slade School of Fine Art (1951–54). He was awarded a scholarship by the French Government in 1954, and a Boise Travelling Scholarship in 1957, which enabled him to travel and work in France, Spain and Italy. An influential teacher, with various positions at Ealing, Wimbledon and Chelsea Schools of Art, Cohen was appointed Professor and Director of the Slade School of Fine Art from 1988–2000.

In 1958 he held his first solo exhibitions in Nottingham at the Midland Group and in London at Gimpel Fils. Cohen’s work has been exhibited widely as part of several international touring British Council exhibitions. Other notable exhibitions include ‘Five Young British Artists’, the 1966 Venice Biennale's British Pavilion show and a retrospective at the Hayward Gallery in 1972. His work is held in numerous collections including the British Council, the Tate, the Victoria & Albert Museum and MoMA.

Cohen currently lives and works in London and continues to exhibit his work widely with exhibitions in 2018 including a Spotlight Display at Tate Britain (2017–18) and a joint exhibition with his son at Flowers Gallery: ‘Bernard & Nathan Cohen: Two Journeys’ (2018).